Fuel will still be available, arguably for centuries. It may well cost a pretty penny in future decades though, so I can foresee more and more of the less valuable classics being converted to electricity.
Indeed, taking the wider view we can pretty much guarantee that oil will be dug out the ground to make peteol or diesel. If every car in the UK - just the cars - were replaced one for one with an electric car then that alone would have consumed more than half the worlds supply of lithium. Clearly that doesnt leave enough for the rest of the world to all have electeic cars, so by default they'll all carry on driving ICE cars, thus perpetuating the demand for fossil fuels or their synthetic equivalent.
Electric cars solve nothing - in NET terms they're little better than ICE cars, they still cause congestion and danger, they still require an excessively large infrastructure. The only genuine solution is a lot less unnecessary private car use, and when it eventually becomes too difficult of expensive then race tracks may I deed become busier again as people go their to practice the historic art of car driving.